Conditions for coherence transformations under incoherent operations
Shuanping Du, Zhaofang Bai, Yu Jing Guo · Physical Review A · 2015
We build in this paper the counterpart of the celebrated Nielsen theorem for coherence manipulation. This offers an affirmative answer to the open question: whether, given two states $\ensuremath{\rho}$ and $\ensuremath{\sigma}$, either $\ensuremath{\rho}$ can be transformed into $\ensuremath{\sigma}$ or vice versa under incoherent operations [Baumgratz et al., Phys. Rev. Lett. 113, 140401 (2014)]. As a consequence, we find that there exist essentially different types of coherence. Moreover, incoherent operations can be enhanced in the presence of certain coherent states. These extra states are coherent catalysts: they allow uncertain incoherent operations to be realized without being consumed in any way. Our main result also sheds light on the construction of coherence measures.